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Binomials :: randomBinomialIdeal

randomBinomialIdeal -- Random Binomial Ideals

Synopsis

Description

The exponents are drawn at random from {-d,...,d}. All coefficients are set to 1.
i1 : R = QQ[a..x]

o1 = R

o1 : PolynomialRing
i2 : randomBinomialIdeal (R,6,2,4,true)

                     2     2         2 2    2    2 2    2      2 2    2 
o2 = ideal (o*p*w - d , i*u  - d*v, l q  - d j, a e  - o t, n*r w  - u ,
     ------------------------------------------------------------------------
      2 2 2    2       2 2
     a c s  - t , b*c*n o  - 1)

o2 : Ideal of R
i3 : randomBinomialIdeal (R,3,4,10,false)

             2     3 4 3    4 4 4 2   4 3 4 3      4 4 3        2 2 4 2 2 2  
o3 = ideal (a d*e*g k n  - f h j p , b e h l  - c*q r s t*x, d*e f i m n s  -
     ------------------------------------------------------------------------
      2 3 3     4 3 3   4    2 3 2 4
     g q r , a*b i s u*v  - c h m p )

o3 : Ideal of R
This function is mostly for internal testing purposes. Don't expect anything from it.

Caveat

Minimal generators are produced. These can be less than n and of higher degree. They also need not be homogeneous.